Vibration of Strongly Nonlinear Discontinuous Systems

Abstract

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

To the Analysis of Models of Efficient Ultrasonic Technology Machines

“…Специфику технологического процесса можно учесть введением его динамических характеристик [3,4]. Указанные уравнения весьма удобно выписывать в операторной форме, при помощи динамических податливостей [15], ставящих в соответствие силам, приложенным в некоторых характерных точках систем, перемещения в каких-либо других или тех же самых точках. Методы динамических податливостей предполагают, что системы -линейны.…”

“…Как правило, величина k0>>1 и поэтому нелинейные характеристики такого типа называют «сильными» [15]. На рис.3, b показана симметричная сильно нелинейная пороговая характеристика.…”

Effects of mistuning on dynamic behavior of nonlinear cyclic systems with lump masses and cubic nonlinearity

“…A n = a n 2 e jβn (21) By substituting Equation (21) into Equation (20), the following equation is obtained:…”

“…Perturbation methods include for instance the method of averaging, the Lindstedt-Poincare' technique and the method of multiple scales and aim at obtaining asymptotically uniform approximations of the solutions. During the last decade or so, one has witnessed a transition from weakly nonlinear structures to strongly nonlinear structures (by strongly nonlinear systems, a system for which the nonlinear terms are the same order as the linear terms is meant) thanks to the extension of classical perturbation techniques [16,17] and the development of new methodologies [18][19][20][21].…”

Milling gate vibrations analysis via Hilbert-Huang transform

“…Nonlinear industrial systems can be classified as systems designed for work in nonlinear ranges of dynamic characteristics and systems of nonlinear properties resulting from fault appearance. Although the sources of nonlinear properties can vary [1,2,3,4], all the nonlinear systems exhibit some common properties. In general, they do not follow the superposition principle and exhibit complex phenomena unusual for linear systems, such as jumps, self-induced and chaotic vibrations, changes in natural frequencies resulting from changes in excitation amplitudes and coexistence of many stable equilibrium positions.…”